Question

Cinrich Pizzeria is considering expanding operations by establishing a delivery business. This will require the purchase of an oven that will cost $53,000, including installation. The oven is expected to last five years, have a $5,300 residual value, and will be depreciated using the straight-line method. Cash flows associated with the delivery business are as follows:

Item		Year 1			Year 2			Year 3			Year 4			Year 5
Revenue		$68,900			$70,278			$82,929			$93,280			$100,955
Ingredients		(26,606	)		(29,256	)		(32,218	)		(35,450	)		(38,898	)
Salary		(26,394	)		(28,514	)		(30,634	)		(32,754	)		(34,768	)
Additional misc.		(2,226	)		(2,438	)		(2,650	)		(2,862	)		(2,968	)
Residual value														5,300

In addition to the above, there are tax consequences related to the new business, and the company’s tax rate is 20 percent.

Calculate the internal rate of return for the delivery business. (Hint: Try a range of rates between 14 percent and 16 percent.) (Round present value factor calculations to 4 decimal places, e.g. 1.2151 and final answer to 0 decimal places, e.g. 18%.)

The internal rate of return

_________________ %

Should Cinrich Pizzeria invest in the delivery business if the required rate of return is 10 percent?

Cinrich Pizzeria: _____SHOULD or SHOULD NOT_____invest in the delivery business.

Can you PLEASE Show your work step by step? I want to learn to calculate this on my own.

Answer 1

Calculation of IRR -

• IRR is the discount rate that equates the present values of cash inflows with the initial investment associated with a project, thereby causing NPV = 0.
• In simple word Internal Rate of Return is rate at which NPV gets Zero
• The project would qualify to be accepted if the IRR exceeds the required rate of return i.e 10%

We have to discount Cashflow in such a Rate by which NPV of project gets Zero

Step 1: Calculation of Cashflows

• (i) Calculation of EBIT(Earning Before Interest and Tax
  

• Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
  Revenue	68,900	70,278	82,929	93,280	1,00,955
  Total Revenue (A)	68,900	70,278	82,929	93,280	1,00,955
  Ingredients	26,606	29,256	32,218	35,450	38,898
  Salary	26,394	28,514	30,634	32,754	34,768
  Additional Misc	2,226	2,438	2,650	2,862	2,968
  Depreciation on Oven =($53,000-$5300)/5	9,540	9,540	9,540	9,540	9,540
  Total Costs (B)	64,766	69,748	75,042	80,606	86,174
  EBIT (A) - (B)	4,134	530	7,887	12,674	14,781

  
  
• (ii) Calculation of cashflow After tax
  

• Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
  Initial Cost of Investments	-53,000
  EBIT		4,134	530	7,887	12,674	14,781
  Less Tax @ 20%		827	106	1,577	2,535	2,956
  EAT		3,307	424	6,310	10,139	11,825
  Add: Depreciation		9,540	9,540	9,540	9,540	9,540
  Add: Salvage Value						5,300
  Cash Flow After Tax	-53,000	12,847	9,964	15,850	19,679	26,665

Step 2: Calculation of IRR

• Now We have to discount above mentioned cashflow by using discount rate @ 14% and 16% as hint given in question

• Year	Cash Flow	Disc @ 14%	Present Value @ 14%	Disc @ 16%	Present Value @ 16%
  0	-53,000	1	-53,000	1	-53,000
  1	12,847	0.8772	11,269	0.8621	11,075
  2	9,964	0.7695	7,667	0.7432	7,405
  3	15,850	0.6750	10,698	0.6407	10,154
  4	19,679	0.5921	11,652	0.5523	10,869
  5	26,665	0.5194	13,849	0.4761	12,695
  	Net NPV		2,135		-802

• Now as we can see that NPV comes Positive at 14% and negative at 16% so the IRR will between these two discounting rates.

IRR = r - {(PVco - PVcfat)/Delta PV} × Delta r

• where r = Either of the two interest rates used in the formula
• PVco = Present value of cash outlay($ 53,000)
• PVcfat = Present value of cash inflows
• Delta r = Difference in interest rates
• Delta PV = Difference in calculated present values of inflows

IRR = 16% - (53,000 - 52,198) / (55,135 - 52,198) × (16-14)

= 16% - 802 / 2937 × 2

= 16% - 0.55%

= 15.45% ~ 15%

Final Answer at 0 Decimal Point = 15%

• Here IRR( 15 %) exceeds the required rate of return (10%)
• so Cinrich Pizzeria should invest in the delivery buiness.

Working Note

For Student Understanding

• Present value of cash inflows PVcfat @16% = 11,075+7,405+10,154+10,869+12,695 = 52,198
• Present value of cash inflows PVcfat @14%=11,269+7,667+10,698+11,652+13,849 = 55,135